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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
time fractional differential equations  mixedindex problems  analytical solution  asymptotic stability  conservative problems  Hamiltonian problems  energyconserving methods  Poisson problems  Hamiltonian Boundary Value Methods  HBVMs  line integral methods  constrained Hamiltonian problems  Hamiltonian PDEs  highly oscillatory problems  boundary element method  finite difference method  floating strike Asian options  continuous geometric average  barrier options  isogeometric analysis  adaptive methods  hierarchical splines  THBsplines  local refinement  linear systems  preconditioners  Cholesky factorization  limited memory  Volterra integral equations  Volterra integro–differential equations  collocation methods  multistep methods  convergence  Bspline  optimal basis  fractional derivative  Galerkin method  collocation method  spectral (eigenvalue) and singular value distributions  generalized locally Toeplitz sequences  discretization of systems of differential equations  higherorder finite element methods  discontinuous Galerkin methods  finite difference methods  isogeometric analysis  Bsplines  curl–curl operator  time harmonic Maxwell’s equations and magnetostatic problems  low rank completion  matrix ODEs  gradient system  ordinary differential equations  Runge–Kutta  tree  stump  order  elementary differential  edgehistogram  edgepreserving smoothing  histogram specification  initial value problems  onestep methods  Hermite–Obreshkov methods  symplecticity  Bsplines  BS methods  hyperbolic partial differential equations  high order discontinuous Galerkin finite element schemes  shock waves and discontinuities  vectorization and parallelization  high performance computing  generalized Schur algorithm  nullspace  displacement rank  structured matrices  stochastic differential equations  stochastic multistep methods  stochastic Volterra integral equations  meansquare stability  asymptotic stability  numerical analysis  numerical methods  scientific computing  initial value problems  onestep methods  Hermite–Obreshkov methods  symplecticity  Bsplines  BS methods
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Molecular magnets show many properties not met in conventional metallic magnetic materials, i.e. low density, transparency to electromagnetic radiation, sensitivity to external stimuli such as light, pressure, temperature, chemical modification or magnetic/electric fields, and others. They can serve as “functional” materials in sensors of different types or be applied in highdensity magnetic storage or nanoscale devices. Research into moleculebased materials became more intense at the end of the 20th century and is now an important branch of modern science. The articles in this Special Issue, written by physicists and chemists, reflect the current work on molecular magnets being carried out in several research centers. Theoretical papers in the issue concern the influence of spin anisotropy in the low dimensional lattice of the resulting type of magnet, as well as thermodynamics and magnetic excitations in spin trimers. The impact of external pressure on structural and magnetic properties and its underlying mechanisms is described using the example of Prussian blue analogue data. The other functionality discussed is the magnetocaloric effect, investigated in coordination polymers and high spin clusters. In this issue, new molecular magnets are presented: (i) ferromagnetic highspin [Mn6] singlemolecule magnets, (ii) solvatomagnetic compounds changing their structure and magnetism dependent on water content, and (iii) a family of purely organic magnetic materials. Finally, an advanced calorimetric study of anisotropy in magnetic molecular superconductors is reviewed.
Heisenberg  S = 1/2 XXZ model  spin anisotropy  square lattice  chain  rectangular lattice  BerezinskiiKosterlitzThouless phase transition  phase diagram  quantum magnet  molecular magnets  magnetocaloric effect  octacyanometallates  critical behaviour  coordination polymers  manganese(III)  salicylamidoxime  molecular magnetism  singlemolecule magnets  radical anion  redox  magnetism  antiferromagnetic coupling  dioxothiadiazole  molecular magnetism  octacyanotungstate(V)  copper(II)  cyclam  cyano bridge  magnetic properties  ?d system  thermodynamic measurement  superconductivity  antiferromagnetism  single crystal heat capacity measurement  magnetic conductor  molecular magnets  spin clusters  Heisenberg exchange Hamiltonian  thermodynamics  inelastic neutron scattering  exact diagonalization  Prussian blue analogues  effect of high pressure  crystal structure  magnetic properties  superexchange interaction
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeperlevel"" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de BroglieBohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeperlevel questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and nonclassical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
quantum foundations  nonlocality  retrocausality  Bell’s theorem  Bohmian mechanics  quantum theory  surrealistic trajectories  Bell inequality  quantum mechanics  generalized Lagrangian paths  covariant quantum gravity  emergent spacetime  Gaussianlike solutions  entropy and time evolution  resonances in quantum systems  the Friedrichs model  complex entropy.  Bell’s theorem  the causal arrow of time  retrocausality  superdeterminism  toymodels  quantum ontology  subquantum dynamics  microconstituents  emergent spacetime  emergent quantum gravity  entropic gravity  black hole thermodynamics  SternGerlach  trajectories  spin  Bell theorem  fractal geometry  padic metric  singular limit  gravity  conspiracy  free will  number theory  quantum potential  Feynman paths  weak values  Bohm theory  nohiddenvariables theorems  observables  measurement problem  Bohmian mechanics  primitive ontology  Retrocausation  weak values  Stochastic Electrodynamics  quantum mechanics  decoherence  interpretations  pilotwave theory  Bohmian mechanics  Born rule statistics  measurement problem  quantum thermodynamics  strong coupling  operator thermodynamic functions  quantum theory  de Broglie–Bohm theory  contextuality  atomsurface scattering  bohmian mechanics  matterwave optics  diffraction  vortical dynamics  Schrödinger equation  de Broglie–Bohm theory  nonequilibrium thermodynamics  zeropoint field  de Broglie–Bohm interpretation of quantum mechanics  pilot wave  interiorboundary condition  ultraviolet divergence  quantum field theory  Aharonov–Bohm effect  physical ontology  nomology  interpretation  gauge freedom  Canonical Presentation  relational space  relational interpretation of quantum mechanics  measurement problem  nonlocality  discrete calculus  iterant  commutator  diffusion constant  LeviCivita connection  curvature tensor  constraints  Kilmister equation  Bianchi identity  stochastic differential equations  Monte Carlo simulations  Burgers equation  Langevin equation  fractional velocity  interpretations of quantum mechanics  David Bohm  mind–body problem  quantum holism  fundamental irreversibility  spacetime fluctuations  spontaneous state reduction  Poincaré recurrence  symplectic camel  quantum mechanics  Hamiltonian  molecule interference  matterwaves  metrology  magnetic deflectometry  photochemistry  past of the photon  Mach–Zehnder interferometer  Dove prism  photon trajectory  weak measurement  transition probability amplitude  atomic metastable states  Bell’s theorem  Bohmian mechanics  nonlocality  many interacting worlds  wavefunction nodes  bouncing oil droplets  stochastic quantum dynamics  de Broglie–Bohm theory  quantum nonequilibrium  Htheorem  ergodicity  ontological quantum mechanics  objective nonsignaling constraint  quantum inaccessibility  epistemic agent  emergent quantum state  selfreferential dynamics  dynamical chaos  computational irreducibility  undecidable dynamics  Turing incomputability  quantum ontology  nonlocality  timesymmetry  retrocausality  quantum causality  conscious agent  emergent quantum mechanics  Bohmian mechanics  de BroglieBohm theory
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